In this talk I will discuss the notion of a GREG — a Group Random Element Generator — which is a generalization of a random walk on a group. Roughly, a Greg is a random sequence of group elements.
Associated with a Greg one obtains a pair of Furstenberg-Poisson boundaries, the spaces of ideal futures and ideal pasts. An important property that a Greg might have is the Asymptotic Past And Future Independence. Gregs satisfying this property, namely Apafic Gregs, are very well behaved. Geodesic Flows in a negatively curved environment, as well as classical random walks on groups, give rise to Apafic Gregs. After surveying the subject, I will focus on linear representations of Gregs and the associated invariant called the Lyapunov spectrum. As it turns out, under mild assumptions the Lyapunov spectrum would be simple and continuously varying.
The talk is based on joint work with Alex Furman.
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IHES Covid-19 regulations:
- all the participants who will attend the event in person will have to keep their mask on in indoor spaces
and where the social distancing is not possible;
- speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable
without it;
- Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass
- Over 25 persons in the conference room, every participant will be asked to provide a health pass which will
be checked at the entrance of the conference room.
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Fanny Kassel
